# Math Help - Leslie’s matrix with population growth

1. ## Leslie’s matrix with population growth

I have a Leslie’s matrix with population growth for this year.

0 2 3 240
0.2 0 0 400
0 0.5 0 320

Next year’s population is
1200
200
160
Because
2*240 +3*240 = 1200
0.2*400 = 200
0.5*320 = 160

How can I calculate population in 50 years?
Thank you.

2. ## Re: Leslie’s matrix with population growth

Originally Posted by mathproblems
I have a Leslie’s matrix with population growth for this year.

0 2 3 240
0.2 0 0 400
0 0.5 0 320

Next year’s population is
1200
200
160
Because
2*240 +3*240 = 1200
0.2*400 = 200
0.5*320 = 160

How can I calculate population in 50 years?

It should be
$2(400)+3(320)$
$(0.2)(240)$
$(0.5)(400)$

$\left( {\begin{array}{rrr} 0 & 2 & 3 \\ {.2} & 0 & 0 \\ 0 & .5 & 0 \\ \end{array} } \right)^{50}$

3. ## Re: Leslie’s matrix with population growth

Originally Posted by Plato

It should be
$2(200)+3(240)$
$(0.2)(240)$
$(0.5)(400)$

$\left( {\begin{array}{rrr} 0 & 2 & 3 \\ {.2} & 0 & 0 \\ 0 & .5 & 0 \\ \end{array} } \right)^{50}$
not sure why do we have 200? 2(200)? and why 320 was not used?
and I am still no sure how to calulate power of 50? Please give me a small hint! Thank you Sir!

4. ## Re: Leslie’s matrix with population growth

Originally Posted by mathproblems
not sure why do we have 200? 2(200)? and why 320 was not used?
and I am still no sure how to calulate power of 50? Please give me a small hint!

Frankly, you post is just too damn hard to read.
I went back to edit my reply.
Why don't you learn LaTex? You can see how easily mine is read.

To do the 50th power you will need a computer algebra system.

See this. also see this

5. ## Re: Leslie’s matrix with population growth

Sorry for the trouble reading my damn questions. Here is one again ...let me rephrase it this time.
The link you sent is great, but how do they calculate? I need to see details...do I need to calculate every year 50 times? (my new damn question LOL)
In my book they skipped the power calculation, just gave the answer after 1 year and then answer for power of 10. (no calculation)

LaTex is nice...but I really do not have time to learn it, trying to keep up with other math stuff.
On a positive note, I understood my mistake above…so now just the power 50 is left.

6. ## Re: Leslie’s matrix with population growth

Originally Posted by mathproblems
LaTex is nice...but I really do not have time to learn it, trying to keep up with other math stuff.

That is absurd. Sometimes spending a little time to make one's life easier, saves ten times in the long term.

7. ## Re: Leslie’s matrix with population growth

It's possible to work out the power by diagonalising the matrix.
Might do this tomorrow, it's after midnight now, and bedtime.

8. ## Re: Leslie’s matrix with population growth

Can someone help me to understand how to calculate population in 50 years?

Thanks!!!

9. ## Re: Leslie’s matrix with population growth

Originally Posted by mathproblems
Can someone help me to understand how to calculate population in 50 years?

It is done here for you.